Hi DG - it's frustrating, isn't it? If I may, I'd suggest backing up just a bit. We could suggest lots of things, but if other stuff is not right, you might fail again.

Before you start, since you are very new, maybe it would be good to verify the basics are in place: good light, good soil mix, know how to water, understand fertilizing in a container, how to set up the container and deal with any limitations or get another container, etc. How comfortable do you feel with those things? You don't have to know what an expert like Al/Tapla knows (or the many others here, also), but the basics are important!

Some flowers are really, really easy and a child might enjoy them blooming and watching bees or butterflies by them. Some herbs are like weeds and almost impossible to kill.

I bet this can be a lot of fun and you and your child will love it.

As for the rain, that's the great thing about having containers, specially relatively small ones like you are talking about. If it's raining a bunch, move the pot. If there is a frost, move the pot. By using containers, we're able to control a lot of what mother nature throws at us. Not everything, but a lot. Judging from your comments about rain, I'd assume you aren't the greatest at watering habits, or you probably would have moved those pots when it kept raining. Don't worry, I'm not that good either at times.

You should probably understand that container gardening requires some more attention, especially with watering and temperatures, than in ground does. We also need to provide nutrients to our container plants. The ground isn't there to give them any of those.

That said, as LO said above, there are some really easy things you can start out with. Lots and lots of flowers are pretty tolerant to swings in environment. Their pretty too! Just look for something that matches your sun and watering requirements.

I'd also suggest some herbs. Try some mint? It can actually be useful in the kitchen, looks nice, and is pretty hard to kill. In fact, it's pretty much a weed, and will fill your container pretty quickly. You can always trim it back though. If you protect it from anything too crazy over the winter, it will grow next year too. You can take it inside if that is easier depending on where you live and the winter weather. Sage might fit in there pretty well also. About the same as mine, only I don't like the looks as much, but you might!

Even with a small container, you could build a little herb garden, and supply your kitchen with some nice stuff. Make sure your mix drains well though, herbs don't like a lot of water. If it rains, put the pot under something, like on the porch or whatever. You control the moisture, not the weather.

I like rosemary, and find it very useful in the kitchen. It's a little slow growing though, and a child may not be entertained by it much.

You might go to a good nursery, ask them. They'll know what plants/flowers are maintenance free in your area. They can even show you what they look like.

Have fun, and remember that so much of gardening is trial and error. It's black magic, and as much as we think we know, it only goes so far.

I think the suggestion of going to a nursery in your area is a good one. Bypass the teens hired for labor and seek out the old guy/gal and explain to him/her what you explained to us. I bet you get some great tips and come home with suitable plants.